# Arbitrage Portfolio Theory (APT) – A Multifactor Macroeconomic Model

• Arbitrage Portfolio Theory (APT) came along after CAPM as a multifactor model to explain returns.

• APT explains returns under the construct where:

• Multiple risks with an excess return above the risk free rate of return can be priced.

• Any security or portfolio has its own beta coefficient to each of the priced risk variables in the model.

• There is a linear relationship between the security's return and the priced risk (a basic assumption of multi-variable regression).

• APT calculates the alpha value, or y-intercept of the model graph.

## Comparing CAPM vs. APT

APT is less restrictive in CAPM, as:

• Asset returns can be described using a multifactor model (CAPM being a single factor model).

• Diversification eliminates the security specific risk of the individual securities in a multi-asset portfolio.

• Assets are priced such that arbitrage profit does not exist.

• The factor sensitivities of the assets in an arbitrage portfolio equal zero and the portfolios expected return is zero.

• Note: If the investor believes that the expected return on the arbitrage portfolio is not equal to zero, then a single factor or multifactor APT style model can be used to capture risk free profit.

• Step 1: Identify and purchase the undervalued asset or portfolio.

• Step 2: Finance the long position with a short sale of overvalued assets.

• Step 3: Close the long and short positions once the assets return to their APT determined equilibrium model values for zero return.

• Whenever two portfolios have the same risk but different expected returns or the same expected return, but different risks, an arbitrage opportunity may be possible.

• It is important to note a couple of key differences between CAPM and APT as these modeling techniques and their variations are extensive in financial research.

• CAPM assumes that investors agree on asset returns, risks, and correlations: E(R), σ, and ρ.

• APT does not assume this, making the theory less restrictive than CAPM.

• CAPM assumes that all investors should construct a portfolio based on the risk free asset and the market portfolio.

• APT does not necessarily assume this

• Other Challenges for CAPM vs. Reality:

• CAPM ignores transaction costs and taxes, which is not realistic for investors.

• Investors rarely can borrow at the risk free rate.

• Not all investors can short sell.

• Risk Aversion as Common Ground: Both APT and CAPM assume that investors are risk averse and will take the highest return for a given amount of risk.

## Pricing E(RP) with an APT Model

An APT model can be thought of an equation where alphas (the excess return of the risk factors) are applied to betas (the sensitivity of the portfolio or security to the risk factor itself).

E(RP) = RF + λiβP,i + λjβP,j

• λi = Factor risk premium return above the risk free rate; the compensation to the investor for accepting the risk.
• βP,i = Coefficient representing the portfolio (or security) return's sensitivity to the risk factor